Solve for $x$ and $y$ using elimination. ${-2x+6y = 44}$ ${3x+5y = 60}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-5$ and the bottom equation by $6$ ${10x-30y = -220}$ $18x+30y = 360$ Add the top and bottom equations together. $28x = 140$ $\dfrac{28x}{{28}} = \dfrac{140}{{28}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-2x+6y = 44}\thinspace$ to find $y$ ${-2}{(5)}{ + 6y = 44}$ $-10+6y = 44$ $-10{+10} + 6y = 44{+10}$ $6y = 54$ $\dfrac{6y}{{6}} = \dfrac{54}{{6}}$ ${y = 9}$ You can also plug ${x = 5}$ into $\thinspace {3x+5y = 60}\thinspace$ and get the same answer for $y$ : ${3}{(5)}{ + 5y = 60}$ ${y = 9}$